What you are experiencing is a normal timeout, because of security concerns.
I had to research that a few hours ago for the same reasons. :-)
If you want to avoid the timeouts, then you must sign in on Chrome on both client and remote computers with the same google identifier (i.e. your email).
1 Configure your "remote" computer to accept remote connections
This obviously means you need to physically access that computer.
In the Chrome Remote Desktop page, the section that interests you is the "My Computers" sections.
There, you click on Enable Remote Connection, which will prompt you to create a password. You'll need that password later.
This will install a few things on your computer (I believe it at least changed the registry on my Windows).
2 Configure your "client" computer
In the same Chrome Remote Desktop page, in the section "My Computers", you'll see the computer you just added.
Click on it, enter the code (possibly checking the checkbox to avoid entering the password again at the next connection)
Et voilà...
Source: http://www.howtogeek.com/142146/how-to-use-google-chrome-to-remotely-access-your-computer/